Optical scanning apparatus, multi-beam optical scanning apparatus, and image-forming apparatus

ABSTRACT

Provided are compact, high-definition, optical scanning apparatus and multi-beam scanning apparatus capable of keeping the spot size uniform in the sub-scanning direction throughout the entire, effective scanning area on a surface to be scanned. An optical scanning apparatus has an entrance optical system  11  for guiding light emitted from a light source  1 , to a deflector  5 , and a scanning optical system  6  for focusing the light reflectively deflected by the deflector, on a surface to be scanned  7 . In the optical scanning apparatus, the scanning optical system has a plurality of sagittal asymmetric change surfaces in which curvatures in the sagittal direction change on an asymmetric basis in the meridional direction with respect to the optical axis of the scanning optical system.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to optical scanning apparatus andmulti-beam optical scanning apparatus and, particularly, the inventionis suitably applicable to image-forming apparatus, for example, such aslaser beam printers involving the electrophotographic process, digitalcopiers, and the like, constructed so as to record image information byreflectively deflecting light from light source means by deflectingmeans to optically scan a surface to be scanned, via scanning opticalmeans with the light.

[0003] 2. Related Background Art

[0004] In the optical scanning apparatus such as the laser beamprinters, the digital copiers, etc. heretofore, the image informationwas recorded in such a manner that the light optically modulatedaccording to an image signal and outputted from the light source meanswas periodically deflected by the deflecting means, for example,consisting of a polygon mirror and was converged in a spot shape on asurface of a photosensitive recording medium by the scanning opticalmeans with the fθ characteristics to optically scan the surface.

[0005]FIG. 13 is a schematic diagram to show the principal part of aconventional, optical scanning apparatus. In the same figure a divergingbeam emitted from the light source means 91 is converted into a nearlyparallel beam by a collimator lens 92 and the nearly parallel beam isrestricted in the beam width by a stop 93 to enter a cylindrical lens 94having a predetermined power only in the sub-scanning direction. Thenearly parallel beam entering the cylindrical lens 94 emerges in thestate of the nearly parallel beam in the main scanning section as it is.In the sub-scanning section the beam is converged to be focused into analmost linear image on a deflection facet (reflective surface) 95 a ofan optical deflector 95 consisting of a polygon mirror. Then thescanning optical means (fθ lens system) 96 with the fθ characteristicsguides the beam reflectively deflected by the deflection facet 95 a ofthe optical deflector 95, via a return mirror 98 to a surface ofphotosensitive drum 97 as a surface to be scanned. The optical deflector95 is rotated at nearly equal angular velocity, whereby the beam scansthe surface to be scanned 97 at almost constant speed to record theimage information thereon.

[0006] For compactifying the apparatus from the optical deflector 95 tothe surface to be scanned 97 herein, it is necessary to effect goodcorrection for optical performance of the fθ lens 96 throughout wideangles of view. For example, Japanese Patent Application Laid-Open No.7-113950 discloses an example of correction for curvature of field(image positions) in the sub-scanning direction and at wide angles ofview by provision of only one surface wherein curvatures in the sagittaldirection vary on an asymmetric basis with respect to the optical axisand wherein magnitude relations of curvatures in the sagittal directionare different between on the upper and lower sides of the optical axis.

[0007] There was, however, the problem that nonuniformity of lateralmagnification (which will also be referred to hereinafter as“sub-scanning magnification”) in the sub-scanning direction appearedprominent at wide angles of view and even if the image positions in thesub-scanning direction were corrected the spot size would vary inproportion to sub-scanning magnifications at respective scanningpositions. Further, in the case of the optical scanning apparatus usingmultiple beams, they suffered the problem that with deviation of thesub-scanning magnifications from a fixed value, line pitch intervals inthe sub-scanning direction varied at every scanning position on thesurface to be scanned, during the optical scanning of the surface to bescanned with the plurality of beams, so as to result in irregular pitch.

[0008] The scanning optical means needs to be located near the opticaldeflector in order to decrease the cost by decreasing the size of thelens. However, there was the problem that it increased the sub-scanningmagnification and the asymmetry of the image positions in thesub-scanning direction and the asymmetry of the sub-scanningmagnifications appeared more prominent.

[0009] An object of the present invention is to provide a compact,high-definition, optical scanning apparatus with wide angles of viewcapable of effecting good correction for curvature of field (imagepositions) in the sub-scanning direction and correction to keep thesub-scanning magnification at a fixed value, by constructing thescanning optical means of a plurality of sagittal asymmetric changesurfaces and properly setting the shape of each lens.

[0010] Another object of the present invention is to provide a compact,high-definition, multi-beam optical scanning apparatus with wide anglesof view capable of keeping line pitch intervals in the sub-scanningdirection constant throughout the entire, effective scanning area, byconstructing the scanning optical means of a plurality of sagittalasymmetric change surfaces and properly setting the shape of each lens.

SUMMARY OF THE INVENTION

[0011] A scanning optical apparatus according to one aspect of theinvention is an optical scanning apparatus comprising entrance opticalmeans for guiding light emitted from light source means, to deflectingmeans, and scanning optical means for focusing the light reflectivelydeflected by the deflecting means, on a surface to be scanned,

[0012] wherein the scanning optical means comprises a plurality ofsagittal asymmetric change surfaces in which curvatures in the sagittaldirection change on an asymmetric basis in the meridional direction withrespect to the optical axis of the scanning optical means.

[0013] In the optical scanning apparatus according to another aspect ofthe invention, said sagittal asymmetric change surfaces comprise two ormore sagittal modification surfaces in which magnitude relation differsamong curvatures in the sagittal direction at respective positions inthe meridional direction with respect to the optical axis.

[0014] In the optical scanning apparatus according to another aspect ofthe invention, said sagittal deformation surfaces comprise two or moresurfaces in which the curvatures in the sagittal direction at therespective positions in the meridional direction with respect to theoptical axis become large or small on the same side.

[0015] In the optical scanning apparatus according to another aspect ofthe invention, in at least one surface of said sagittal deformationsurfaces the curvatures in the sagittal direction become large on theside of said light source means with respect to the optical axis.

[0016] In the optical scanning apparatus according to another aspect ofthe invention, in at least one surface of said sagittal asymmetricchange surfaces the curvatures in the sagittal direction have aninflection point only on one side in the meridional direction withrespect to the optical axis.

[0017] In the optical scanning apparatus according to another aspect ofthe invention, said scanning optical means comprises a plurality of fθlenses, an fθ lens located closest to the deflecting means out of saidplurality of fθ lenses has a negative, refractive power in thesub-scanning direction, and an fθ lens located closest to the surface tobe scanned has a positive, refractive power in the sub-scanningdirection.

[0018] In the optical scanning apparatus according to another aspect ofthe invention, all lens surfaces of said plurality of fθ lenses areformed in a concave shape opposed to said deflecting means.

[0019] In the optical scanning apparatus according to another aspect ofthe invention, the following condition is satisfied:

k/W≦0.6

[0020] where k is an fθ coefficient of said scanning optical means and Wan effective scanning width on said surface to be scanned.

[0021] In the optical scanning apparatus according to another aspect ofthe invention, the following condition is satisfied:

|β_(s)|≧2

[0022] where β_(s) is a lateral magnification in the sub-scanningdirection of said scanning optical means.

[0023] A multi-beam optical scanning apparatus according to a furtheraspect of the invention is a multi-beam optical scanning apparatuscomprising light source means having a plurality of light-emittingregions, entrance optical means for guiding a plurality of beams emittedfrom the light source means, to deflecting means, and scanning opticalmeans for focusing the plurality of beams reflectively deflected by thedeflecting means, on a surface to be scanned,

[0024] wherein said scanning optical means comprises a plurality ofsagittal asymmetric change surfaces in which curvatures in the sagittaldirection change on an asymmetric basis in the meridional direction withrespect to the optical axis of the scanning optical means.

[0025] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, said sagittal asymmetric change surfacescomprise two or more sagittal modification surfaces in which magnituderelation differs among curvatures in the sagittal direction atrespective positions in the meridional direction with respect to theoptical axis.

[0026] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, said sagittal deformation surfaces comprise twoor more surfaces in which the curvatures in the sagittal direction atthe respective positions in the meridional direction with respect to theoptical axis become large or small on the same side.

[0027] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, in at least one surface of said sagittaldeformation surfaces the curvatures in the sagittal direction becomelarge on the side of said light source means with respect to the opticalaxis.

[0028] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, in at least one surface of said sagittalasymmetric change surfaces the curvatures in the sagittal direction havean inflection point only on one side in the meridional direction withrespect to the optical axis.

[0029] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, said scanning optical means comprises aplurality of fθ lenses, an fθ lens located closest to the deflectingmeans out of said plurality of fθ lenses has a negative, refractivepower in the sub-scanning direction, and an fθ lens located closest tothe surface to be scanned has a positive, refractive power in thesub-scanning direction.

[0030] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, all lens surfaces of said plurality of fθlenses are formed in a concave shape opposed to said deflecting means.

[0031] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, the following condition is satisfied:

k/W≦0.6

[0032] where k is an fθ coefficient of said scanning optical means and Wan effective scanning width on said surface to be scanned.

[0033] In the multi-beam optical scanning apparatus according to anotheraspect of the invention, the following condition is satisfied:

[0034] where β_(s) is a lateral magnification in the sub-scanningdirection of said scanning optical means.

[0035] An image-forming apparatus according to a further aspect of theinvention is an image-forming apparatus comprising the scanning opticalapparatus as set forth, a photosensitive body located at said surface tobe scanned, a developing unit for developing an electrostatic, latentimage-formed on said photosensitive body with the light under scan bysaid scanning optical apparatus, into a toner image, a transfer unit fortransferring said developed toner image onto a transfer medium, and afixing unit for fixing the transferred toner image on the transfermedium.

[0036] Another image-forming apparatus according to a further aspect ofthe present invention is an image-forming apparatus comprising thescanning optical apparatus as set forth, and a printer controller forconverting code data supplied from an external device, into an imagesignal and supplying the image signal to said scanning opticalapparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

[0037]FIG. 1 is a cross-sectional view along the main scanning directionof the optical scanning apparatus in Embodiment 1 of the presentinvention;

[0038]FIG. 2 is a cross-sectional view along the sub-scanning directionof the optical scanning apparatus in Embodiment 1 of the presentinvention;

[0039]FIG. 3 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 1 of the present invention;

[0040]FIG. 4 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 1 of the present invention;

[0041]FIG. 5 is an aberration diagram of the scanning optical means inEmbodiment 1 of the present invention;

[0042]FIG. 6 is an aberration diagram of the scanning optical means inEmbodiment 1 of the present invention, and a comparative example;

[0043]FIG. 7 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 2 of the present invention;

[0044]FIG. 8 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 2 of the present invention;

[0045]FIG. 9 is an aberration diagram of the scanning optical means inEmbodiment 2 of the present invention;

[0046]FIG. 10 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 3 of the present invention;

[0047]FIG. 11 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 3 of the present invention;

[0048]FIG. 12 is an aberration diagram of the scanning optical means inEmbodiment 3 of the present invention;

[0049]FIG. 13 is a schematic diagram of principal part to show aconventional, optical scanning apparatus; and

[0050]FIG. 14 is a schematic diagram of an image-forming apparatus ofthe present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiment 1

[0051]FIG. 1 is a cross-sectional view of the principal part along themain scanning direction (a main scanning section) of the opticalscanning apparatus in Embodiment 1 of the present invention and FIG. 2is a cross-sectional view of the principal part along the sub-scanningdirection (a sub-scanning section) of FIG. 1.

[0052] In the present specification the main scanning direction(meridional direction) is defined along the direction into which thelight is reflectively deflected (or deflected to scan) by the deflectingmeans, and the sub-scanning direction (sagittal direction) along thedirection perpendicular to the optical axis of the scanning opticalmeans and to the main scanning direction.

[0053] In the figures, numeral 1 designates a light source means, whichis comprised, for example, of a semiconductor laser. Numeral 2 denotes acollimator lens (condenser lens), which converts a diverging beam (lightbeam) emitted from the light source means 1 into a nearly parallel beam.Numeral 3 represents an aperture stop, which limits passing light(amount of light). Numeral 4 indicates a cylindrical lens (anamorphiclens), which has a predetermined power only in the sub-scanningdirection and which focuses the beam having passed the aperture stop 3in an almost linear image on a deflection facet (reflective surface) 5 aof an optical deflector 5 described hereinafter, in the sub-scanningsection. Each of the elements including the collimator lens 2, theaperture stop 3, the cylindrical lens 4, and so on constitutes anelement of entrance optical means 11.

[0054] Numeral 5 denotes the optical deflector as the deflecting means,which is comprised, for example, of a polygon mirror (rotary polygonmirror) and which is rotated at a fixed speed in the direction of arrowA in the drawing by a driving means such as a motor or the like (notillustrated).

[0055] Numeral 6 denotes the scanning optical means having theconverging function and the fθ characteristics, which has first andsecond fθ lenses (scanning lenses) 6 a, 6 b of the shape describedhereinafter, which focuses the beam based on the image information,which was reflectively deflected by the optical deflector 5, on aphotosensitive drum surface 7 as a surface to be scanned, and which hasan inclination correcting function by keeping the deflection facet 5 aof the optical deflector 5 in conjugate with the surface to be scanned 7in the sub-scanning section. In the scanning optical means 6 the firstfθ lens 6 a on the side of optical deflector 5 has a negative,refractive power in the sub-scanning direction and the second fθ lens 6b on the side of the surface to be scanned 7 has a positive, refractivepower in the sub-scanning direction.

[0056] Numeral 7 represents a surface of a photosensitive drum (asurface of an image carrier) as a surface to be scanned.

[0057] In the present embodiment the diverging beam emitted from thesemiconductor laser 1 is converted into a nearly parallel beam by thecollimator lens 2 and the beam (amount of light)is limited by theaperture stop 3 to enter the cylindrical lens 4. The nearly parallelbeam entering the cylindrical lens 4 emerges in the as-entering state inthe main scanning section. In the sub-scanning section the beam isconverged to be focused as an almost linear image (a linear imagelongitudinal in the main scanning direction) on the deflection facet 5 aof the optical deflector 5. Then the beam reflectively deflected by thedeflection facet 5 a of the optical deflector 5 travels through thefirst fθ lens 6 a and the second fθ lens 6 b to be focused in a spotshape on the surface of the photosensitive drum 7. The optical deflector5 is rotated in the direction of arrow A, whereby the beam opticallyscans the surface of the photosensitive drum 7 at an equal speed in thedirection of arrow B (in the main scanning direction). This causes animage to be recorded on the photosensitive drum surface 7 as a recordingmedium.

[0058] The optical layout of the scanning optical means 6 and asphericalcoefficients of the first and second fθ lenses 6 a, 6 b in the presentembodiment are presented in Table 1 and Table 2, respectively. FIG. 3and FIG. 4 are drawings to show how curvatures in the sagittal directionvary in each of surfaces of the first and second fθ lenses 6 a, 6 b,respectively, in the present embodiment. TABLE 1 LAYOUT OF OPTICALSCANNING APPARATUS fθ COEFFICIENT (mm/rad) fθ COEFFICIENT k 109WAVELENGTH, REFRACTIVE INDEX WAVELENGTH USED λ (nm) 780 fθ LENS 6aREFRACTIVE INDEX N1 1.5242 fθ LENS 6b REFRACTIVE INDEX N2 1.5242PLACEMENT OF IMAGING OPTICAL SYSTEM (mm) REFLECTIVE SURFACE OF POLYGONd1 10.50 MIRROR 5a-LENS 6a INCIDENCE SURFACE 6ai LENS 6a INCIDENCESURFACE 6ai- d2 7.05 LENS 6a EXIT SURFACE 6ao LENS 6a EXIT SURFACE6ao-LENS d3 6.45 6b INCIDENCE SURFACE 6bi LENS 6b INCIDENCE SURFACE 6bi-d4 7.55 LENS 6b EXIT SURFACE 6bo LENS 6b EXIT SURFACE 6bo- d5 102.45SURFACE TO BE SCANNED 7 EFFECTIVE SCAN WIDTH (mm) W 214 k/W k/W 0.51SUB-SCANNING MAGNIFICATION βs 3.3

[0059] TABLE 2 LAYOUT OF OPTICAL SCANNING APPARATUS fθ LENS 6aMERIDIONAL fθ LENS 6b MERIDIONAL fθ LENS 6a SAGITTAL fθ LENS 6b SAGITTALSHAPE SHAPE SHAPE SHAPE IN- IN- IN- IN- CIDENCE EXIT CIDENCE EXITCIDENCE EXIT CIDENCE EXIT SURFACE SURFACE SURFACE SURFACE SURFACESURFACE SURFACE SURFACE 6ai 6ao 6b1 6bo 6ai 6ao 6bi 6bo ON THE LIGHTSOURCE SIDE R −3.02877E+ −2.16472E+ R 8.14379E+ 7.96757E+ r −1.00000E+−2.32587E+01 r 7.18760E+01 −1.26284E+01 01 01 01 01 01 K −2.52957E+−1.20217E+ K −6.6965E+ −1.39708E− D2 0.00000E+ −1.48301E−03 D2−1.19364E−03 1.44964E−03 00 00 00 01 00 B4 3.61254E− 1.57451E− B4−1.46498E− −2.14482E− D4 0.00000E+ −2.46682E−06 D4 1.96871E−06−2.17689E−06 05 05 05 05 00 B6 −8.09230E− 3.57693E− B6 1.26772E−2.47677E− D6 0.00000E+ 4.91740E−09 D6 −1.63328E−10 2.44849E−09 08 08 0808 00 B8 0.00000E+ −1.12626E− B8 −1.36311E− −2.71180E− D8 0.00000E+1.13169E−11 D8 −1.09555E−13 −1.26980E−12 00 10 12 11 00 B10 0.00000E+0.00000E+ B10 −2.45186E− 2.06855E− D10 0.00000E+ −1.90462E−15 D101.42201E−16 8.86595E−17 00 00 15 14 00 B12 0.00000E+ 0.00000E+ B120.00000E+ −6.92697E− D12 0.00000E+ 0.00000E+00 D12 0.00000E+000.00000E+00 00 00 00 18 00 ON THE OTHER SIDE R −3.02877E+ −2.16472E+ R8.14379E+ 7.96757E+ r −1.00000E+ −2.32587E+01 r 7.18760E+01 −1.26284E+0101 01 01 01 01 K −2.52957E+ −1.20217E+ K −6.69965E+ −1.39708E− D20.00000E+ −6.74273E−03 D2 7.86075E−03 1.44964E−03 00 00 00 01 00 B43.61254E− 1.49085E− B4 −1.63400E− −2.24876E− D4 0.00000E+ 3.13732E−05 D4−1.20370E−05 −2.17689E−06 05 05 05 05 00 B6 −8.09230E− 4.08194E− B61.64210E− 2.67132E− D6 0.00000E+ −4.91023E−08 D6 2.30753E−09 2.44849E−0908 08 08 08 00 B8 0.00000E+ −1.20672E− B8 −4.36204E− −2.94646E− D80.00000E+ −1.96138E−12 D8 1.30133E−12 −1.26980E−12 00 10 12 11 00 B100.00000E+ 0.00000E+ B10 −2.17220E− 2.28464E− D10 0.00000E+ −4.27397E−16D10 4.58193E−15 8.86595E−17 00 00 15 14 00 B12 0.00000E+ 0.00000E+ B120.00000E+ −8.12057E− D12 0.00000E+ 0.00000E+00 D12 0.00000E+000.00000E+00 00 00 00 18 00

[0060] In the present embodiment each of meridional lens shapes of thefirst and second fθ lenses 6 a, 6 b is comprised of an aspherical shapethat can be expressed as a function up to degree 12. For example, let usdefine the origin at an intersection between the optical axis and thefirst or second fθ lens 6 a, 6 b, take the X-axis along the direction ofthe optical axis, and take the Y-axis along an axis perpendicular to theoptical axis in the main scanning section. Then the shapes in themeridional direction corresponding to the main scanning direction areexpressed by the following equation.

X=(Y ² /R)/[1+{1−(1+K)(Y/R)²}^(1/2) ]+B 4×Y ⁴ +B 6×Y ⁶ +B 8×Y ⁸ +B 10×Y¹⁰ +B 12×Y ¹²

[0061] (where R is a radius of curvature in the meridional direction andon the optical axis, and k, B4, B6, B8, B10, and B12 are the asphericalcoefficients)

[0062] Sagittal lines of each lens surface continuously change theirradii of curvatures with change in coordinates on the lens surface inthe main scanning direction. The radius R_(s)* of the curvature of thesagittal line at the position where the coordinate is Y in the mainscanning direction, is expressed by the following equation.

R _(s) *=R _(s)×(1+D 2×Y ² +D 4×Y ⁴ +D 6×Y ⁶ +D 8×Y ⁸ +D 10×Y ¹⁰)

[0063] (where R_(s) is the radius of the curvature in the sagittaldirection and on the optical axis, and D2, D4, D6, D8, and D10 arecoefficients)

[0064] In the present embodiment the first fθ lens 6 a is a positivemeniscus lens with a concave surface opposed to the polygon mirror 5 inthe main scanning section and a negative meniscus lens with a concavesurface opposed to the polygon mirror 5 in the sub-scanning section.

[0065] The second fθ lens 6 b is a positive meniscus lens with a convexsurface opposed to the polygon mirror 5 in the main scanning section anda double-convex lens with a convex surface opposed to the polygon mirror5 and the other convex surface to the surface to be scanned 7 in thesub-scanning section.

[0066] In the incidence surface 6 ai of the first fθ lens 6 a, thesurfaces in the main scanning and sub-scanning directions both aresymmetric in the main scanning direction with respect to the opticalaxis, and the surface consists of a surface of a constant curvature inthe sagittal direction (hereinafter also referred to as “sagittalcurvature”) normal to the meridional line in the main scanning section.

[0067] In the exit surface 6 ao of the first fθ lens 6 a, the surface inthe main scanning direction is asymmetric with respect to the opticalaxis, and the surface in the sub-scanning direction consists of asagittal asymmetric change surface in which curvatures in the sagittaldirection change on an asymmetric basis in the main scanning directionwith respect to the optical axis.

[0068] In the incidence surface 6 bi of the second fθ lens 6 b, thesurface in the main scanning direction is asymmetric with respect to theoptical axis, and the surface in the sub-scanning direction consists ofa sagittal asymmetric change surface in which curvatures in the sagittaldirection change on an asymmetric basis in the main scanning directionwith respect to the optical axis.

[0069] In the exit surface 6 bo of the second fθ lens 6 b, the surfacein the main scanning direction is asymmetric with respect to the opticalaxis, and the surface in the sub-scanning direction consists of asurface in which curvatures in the sagittal direction increase on asymmetric basis in the main scanning direction on either side of theoptical axis.

[0070]FIG. 5 is an aberration diagram to show the curvature of field inthe sub-scanning direction and ratios of sub-scanning magnifications ofthe optical scanning apparatus in the present embodiment. FIG. 6 is adiagram to show the curvature of field in the sub-scanning direction andratios of sub-scanning magnifications in the present embodiment (solidlines) and a comparative example (dashed lines) wherein curvatures inthe sagittal direction on the anti-source side (i.e., on the other sidethan the side of the light source means 1 with respect to the opticalaxis of the scanning optical means 6) are equal to those on the lightsource side (i.e., on the same side as the light source means 1 withrespect to the optical axis of the scanning optical means 6) so that thecurvatures in the sagittal direction of the scanning optical means 6 inthe present embodiment are symmetric in the main scanning direction withrespect to the optical axis in all the four surfaces.

[0071] It is seen from FIG. 5 and FIG. 6 that the curvature of field inthe sub-scanning direction and the asymmetry of sub-scanningmagnifications are corrected well in the present embodiment.

[0072] In the present embodiment, where the fθ coefficient of thescanning optical means 6 is k and the effective scanning width on thesurface to be scanned 7 is W, the following condition is satisfied:

k/W≦0.6.

[0073] When the lateral magnification in the sub-scanning direction ofthe scanning optical means 6 is β_(s), the following condition issatisfied:

|γ_(s)≧2.

[0074] In the present embodiment the fθ coefficient of the scanningoptical means 6 is set to k=109 (mm/rad), the effective scanning widthon the surface to be scanned 7 to W=214 mm, the angles of view to thewide angles of view over ±56°, and the sub-scanning magnification to|β_(s)|=3.3.

[0075] In general, in the optical scanning apparatus, when the lightemitted from the light source means is reflectively deflected at thedeflection facet of the polygon mirror, the position of reflectionvaries depending upon angles of view and deviation of the reflectionposition is asymmetric with respect to the optical axis of the scanningoptical means. This makes the image positions asymmetric in the mainscanning and sub-scanning directions and also makes the sub-scanningmagnifications asymmetric. In the case wherein the angles of view arethe wide angles of view over ±47° and the sub-scanning magnifications(|β_(s)|≧2) are high as in the present embodiment, the asymmetry of thesub-scanning magnifications and the curvature of field (image positions)in the sub-scanning direction appears more prominent.

[0076] In the present embodiment the scanning optical means 6 is thusconstructed of the combination of the surfaces wherein the curvatures inthe sagittal direction change on an asymmetric basis as described above,whereby the asymmetry of the sub-scanning magnifications and thecurvature of field (image positions) in the sub-scanning direction canbe corrected well even in the case of the wide angles of view and thehigh sub-scanning magnifications. This permits the spot size in thesub-scanning direction to be kept constant at all the scanning positionsin the effective scanning area on the surface to be scanned.

[0077] In the present embodiment, as described above, the scanningoptical means 6 is thus constructed of the plurality of sagittalasymmetric change surfaces and the shape of each lens is properly set,whereby the curvature of field is corrected well in the sub-scanningdirection while the image magnifications in the sub-scanning directionare corrected into a constant value, so as to make the spot size uniformin the sub-scanning direction.

[0078] In the present embodiment the scanning optical means 6 wasconstructed of the two fθ lenses 6 a, 6 b, but the present invention isnot limited to this example; for example, the present invention can alsobe applied to configurations in which the scanning optical means 6 iscomposed of one fθ lens or of three or more fθ lenses, similarly as inabove Embodiment 1.

Embodiment 2

[0079] Described next is the multi-beam optical scanning apparatus inEmbodiment 2 of the present invention.

[0080] The present embodiment is different from above Embodiment 1 inthat the light source means 1 is comprised of a multi beam semiconductorlaser consisting of two light-emitting regions and in that degrees ofchange are different for the curvatures in the sagittal direction in thesurfaces of the first and second fθ lenses 6 a, 6 b constituting thescanning optical means 6. The other structure and optical action aresubstantially the same as in Embodiment 1, thereby achieving likeeffect.

[0081] The optical layout of the scanning optical means 6 and theaspherical coefficients of the first and second fθ lenses 6 a, 6 b inthe present embodiment are presented in Table 3 and Table 4,respectively. FIG. 7 and FIG. 8 are diagrams to show how the curvaturesin the sagittal direction change in each of the surfaces of the firstand second fθ lenses 6 a, 6 b, respectively, in the present embodiment.TABLE 3 LAYOUT OF OPTICAL SCANNING APPARATUS fθ COEFFICIENT (mm/rad) fθCOEFFICIENT k 109 WAVELENGTH, REFRACTIVE INDEX WAVELENGTH USED λ (nm)780 fθ LENS 6a REFRACTIVE INDEX N1 1.5242 fθ LENS 6b REFRACTIVE INDEX N21.5242 PLACEMENT OF IMAGING OPTICAL SYSTEM (mm) REFLECTIVE SURFACE OFPOLYGON d1 10.50 MIRROR 5a-LENS 6a INCIDENCE SURFACE 6ai LENS 6aINCIDENCE SURFACE 6ai- d2 7.05 LENS 6a EXIT SURFACE 6ao LENS 6a EXITSURFACE 6ao-LENS d3 6.45 6b INCIDENCE SURFACE 6bi LENS 6b INCIDENCESURFACE 6bi- d4 7.55 LENS 6b EXIT SURFACE 6bo LENS 6b EXIT SURFACE 6bo-d5 102.45 SURFACE TO BE SCANNED 7 EFFECTIVE SCAN WIDTH (mm) W 214 k/Wk/W 0.51 SUB-SCANNING MAGNIFICATION βs 3.3

[0082] TABLE 4 LAYOUT OF OPTICAL SCANNING APPARATUS fθ LENS 6aMERIDIONAL fθ LENS 6b MERIDIONAL fθ LENS 6a SAGITTAL fθ LENS 6b SAGITTALSHAPE SHAPE SHAPE SHAPE IN- IN- IN- IN- CIDENCE EXIT CIDENCE EXITCIDENCE EXIT CIDENCE EXIT SURFACE SURFACE SURFACE SURFACE SURFACESURFACE SURFACE SURFACE 6ai 6ao 6bi 6bo 7ai 6ao 6bi 6bo ON THE LIGHTSOURCE SIDE R −3.02877E+ −2.16472E+ R 8.14379E+ 7.96757E+ r −1.00000E+−2.32587E+01 r 7.18760E+01 −1.26284E+01 01 01 01 01 01 K −2.52957E+−1.20217E+ K −6.69965E+ −1.39708E+ D2 4.28806E− 1.94201E−03 D2−1.36754E−03 1.31246E−03 00 00 00 01 03 B4 3.61254E− 1.57451E− B4−1.46498E− −2.14482E− D4 0.00000E+ −2.44214E−06 D4 2.41168E−06−1.74690E−06 05 05 05 05 00 B6 −8.09230E− 3.57693E− B6 1.26772E−2.47677E− D6 0.00000E+ −3.45544E−08 D6 −5.36054E−10 1.72030E−09 08 08 0808 00 B8 0.00000E+ −1.12626E− B8 −1.36311E− −2.71180E− D8 0.00000E+7.76111E−11 D8 −2.34886E−13 −8.99867E−13 00 10 12 11 00 B10 0.00000E+0.00000E+ B10 −2.45186E− 2.06855E− D10 0.00000E+ −1.84716E−15 D101.12331E−16 1.13837E−16 00 00 15 14 00 B12 0.00000E+ 0.00000E+ B120.00000E+ −6.92697E+ D12 0.00000E+ 0.00000E+00 D12 0.00000E+000.00000E+00 00 00 00 18 00 ON THE OTHER SIDE R −3.02877E+ −2.16472E+ R8.14379E+ 7.96757E+ r −1.00000E+ −2.09964E+01 r 6.48557E+01 −1.30869E+0101 01 01 01 01 K −2.52957E+ −1.20217E+ K −6.69965E+ −1.39708E− D20.00000E+ −6.25001E−03 D2 9.15047E−03 1.31246E−03 00 00 00 01 00 B43.61254E− 1.49085 B4 −1.63400E− −2.24876E− D4 0.00000E+ 2.87184E−05 D4−1.10470E−05 −1.74690E−06 05 05 05 05 00 B6 −8.09230E− 4.08194E− B61.64210E− −2.67132E− D6 0.00000E+ −4.47732E−08 D6 2.23789E−091.72030E−09 08 08 08 08 00 B8 0.00000E+ −1.20672E− B8 −4.36204E−−2.94646E− D8 0.00000E+ −1.98582E−12 D8 1.28175E−12 −8.99867E−13 00 1012 11 00 B10 0.00000E+ 0.00000E+ B10 −2.17220E− 2.28464E− D10 0.00000E+−4.28401E−16 D10 4.13805E−15 1.13837E−16 00 00 15 14 00 B12 0.00000E+0.00000E+ B12 0.00000E+ −8.12057E− D12 0.00000E+ 0.00000E+00 D120.00000E+00 0.00000E+00 00 00 00 18 00

[0083] In the present embodiment, in the incidence surface 6 ai of thefirst fθ lens 6 a, the surface in the sub-scanning direction consists ofa sagittal asymmetric change surface in which curvatures in the sagittaldirection change on an asymmetric basis in the main scanning directionwith respect to the optical axis. Further, the magnitude relation amongthe curvatures in the sagittal direction is as follows.

[0084] curvatures on the light source side>curvature on the opticalaxis=curvatures on the anti-source side

[0085] Therefore, the surface is also a sagittal deformation surface inwhich the magnitude relation differs among the curvatures in thesagittal direction at respective positions in the main scanningdirection with respect to the optical axis.

[0086] In the exit surface 6 ao of the first fθ lens 6 a, the surface inthe sub-scanning direction consists of a sagittal asymmetric changesurface in which the curvatures in the sagittal direction change on anasymmetric basis in the main scanning direction with respect to theoptical axis.

[0087] Further, the magnitude relation among the curvatures in thesagittal direction is as follows.

[0088] curvatures on the light source side>curvature on the opticalaxis>curvatures on the anti-source side.

[0089] Thus, the surface is also a sagittal deformation surface in whichthe magnitude relation differs among the curvatures in the sagittaldirection at respective positions in the main scanning direction withrespect to the optical axis.

[0090] In the incidence surface 6 bi of the second fθ lens 6 b, thesurface in the sub-scanning direction consists of a sagittal asymmetricchange surface in which the curvatures in the sagittal direction changeon an asymmetric basis in the main scanning direction with respect tothe optical axis and is also a sagittal deformation surface in which thecurvatures in the sagittal direction increase with distance from theoptical axis up to an inflection point at a middle point and thengradually decrease on the side of light source means 1 with respect tothe optical axis while the curvatures gradually decrease with distancefrom the optical axis on the other side than the side of light sourcemeans 1 (see FIG. 8).

[0091] In the exit surface 6 bo of the second fθ lens 6 b, the surfacein the sub-scanning direction consists of a surface in which thecurvatures in the sagittal direction increase on a symmetric basis inthe main scanning direction on either side of the optical axis.

[0092]FIG. 9 is an aberration diagram to show the curvature of field inthe sub-scanning direction and ratios of sub-scanning magnifications ofthe optical scanning apparatus in the present embodiment.

[0093] In the present embodiment the curvatures in the sagittaldirection are largely changed in the incidence surface 6 ai and the exitsurface 6 ao of the first fθ lens 6 a and the incidence surface 6 bi ofthe second fθ lens 6 b, whereby better correction can be made for thecurvature of field in the sub-scanning direction and the ratios ofsub-scanning magnifications.

[0094] Specifically, the position of the principal plane is largelymoved by making the curvatures in the sagittal direction on the side ofthe light source means 1 in the incidence surface 6 ai and the exitsurface 6 ao of the first fθ lens 6 a and the incidence surface 6 bi ofthe second fθ lens 6 b all larger than the corresponding curvature inthe sagittal direction on the optical axis and making the curvatures inthe sagittal direction on the anti-source side in the exit surface 6 aoof the first fθ lens 6 a and the incidence surface 6 bi of the second fθlens 6 b both smaller than the corresponding curvature in the sagittaldirection on the optical axis, whereby correction is made to make thecurvature of field in the sub-scanning direction and the sub-scanningmagnifications constant. The present embodiment makes more accuratecorrection feasible by changing the curvatures in the sagittal directionon either one side in the main scanning direction with respect to theoptical axis so as to have the inflection point midway as in the stateof change of the curvatures in the sagittal direction on the lightsource means 1 side in the incidence surface 6 bi of the second fθ lens6 b.

[0095] This permits the present embodiment to keep the spot sizes of aplurality of beams in the sub-scanning direction constant irrespectiveof the scanning positions in the effective scanning area on the surfaceto be scanned 7 and to keep the line pitch intervals constantirrespective of the scanning positions on the surface to be scanned 7during the optical scanning of the surface to be scanned 7 with thebeams, thereby realizing the multi-beam optical scanning apparatuscapable of always obtaining good images without pitch irregularity.

Embodiment 3

[0096] Described next is the multi-beam optical scanning apparatus inEmbodiment 3 of the present invention.

[0097] The present embodiment is different from above Embodiment 2 inthat all the lens surfaces of the first and second fθ lenses 6 a, 6 bconstituting the scanning optical means 6 are formed in the concaveshape opposed to the optical deflector 5 and in that degrees of changein the curvatures in the sagittal direction are different. The otherstructure and optical action are substantially the same as in Embodiment2, thereby achieving like effect.

[0098] The optical layout of the scanning optical means 6 and theaspherical coefficients of the first and second fθ lenses 6 a, 6 b inthe present embodiment are presented in Table 5 and Table 6,respectively. FIG. 10 and FIG. 11 are diagrams to show how thecurvatures in the sagittal direction change in each of the surfaces ofthe first and second fθ lenses 6 a, 6 b, respectively, in the presentembodiment. TABLE 5 LAYOUT OF OPTICAL SCANNING APPARATUS fθ COEFFICIENT(mm/rad) fθ COEFFICIENT k 109 WAVELENGTH, REFRACTIVE INDEX WAVELENGTHUSED λ (nm) 780 fθ LENS 6a REFRACTIVE INDEX N1 1.5242 fθ LENS 6bREFRACTIVE INDEX N2 1.5242 PLACEMENT OF IMAGING OPTICAL SYSTEM (mm)REFLECTIVE SURFACE OF POLYGON d1 10.50 MIRROR 5a-LENS 6a INCIDENCESURFACE 6ai LENS 6a INCIDENCE SURFACE 6ai- d2 7.05 LENS 6a EXIT SURFACE6ao LENS 6a EXIT SURFACE 6ao-LENS d3 6.45 6b INCIDENCE SURFACE 6bi LENS6b INCIDENCE SURFACE 6bi- d4 7.55 LENS 6b EXIT SURFACE 6bo LENS 6b EXITSURFACE 6bo- d5 102.45 SURFACE TO BE SCANNED 7 EFFECTIVE SCAN WIDTH (mm)W 214 k/W k/W 0.51 SUB-SCANNING MAGNIFICATION βs 3.1

[0099] TABLE 6 LAYOUT OF OPTICAL SCANNING APPARATUS fθ LENS 6aMERIDIONAL fθ LENS 6b MERIDIONAL fθ LENS 6a SAGITTAL fθ LENS 6b SAGITTALSHAPE SHAPE SHAPE SHAPE IN- IN- IN- IN- CIDENCE EXIT CIDENCE EXITCIDENCE EXIT CIDENCE EXIT SURFACE SURFACE SURFACE SURFACE SURFACESURFACE SURFACE SURFACE 6ai 6ao 6bi 6bo 6ai 6ao 6bi 6bo ON THE LIGHTSOURCE SIDE R −3.02877E+ −2.16472E+ R 8.14379E+ 7.96757E+ r −1.00000E+−2.12739E+01 r −5.12420E+01 −1.00000E+01 01 01 01 01 01 K −2.52957E+−1.20217E+ K −6.69965E+ −1.39708E− D2 1.48475E− 1.37384E−02 D21.35236E−02 1.507729E−03 00 00 00 01 02 B4 3.61254E− 1.57451E− B4−1.46498E− −2.14482E− D4 0.00000E+ −8.27842E−07 D4 −2.66781E−05−4.37989E−06 05 05 05 05 00 B6 −8.09230E− 3.57693E− B6 1.26772E−2.47677E− D6 0.00000E+ −8.53731E−11 D6 −2.05461E−09 7.77917E−09 08 08 0808 00 B8 0.00000E+ −1.12626E− B8 −1.36311E− −2.71180E− D8 0.00000E+4.2219E−10 D8 1.19594E−10 −6.41723E−12 00 10 12 11 00 B10 0.00000E+0.00000E+ B10 −2.45186E− 2.06855E− D10 0.00000E+ 0.00000E−00 D103.72456E−14 1.95495E−15 00 00 15 14 00 B12 0.00000E+ 0.00000E+ B120.00000E+ −6.92697E− D12 0.00000E+ 0.00000E+00 D12 0.00000E+000.00000E+00 00 00 00 18 00 ON THE OTHER SIDE R −3.02877E+ −2.16472E+ R8.14379E+ 7.96757E+ r −1.00000E+ −2.12739E+01 r −5.12420E+01−1.00000E+01 01 01 01 01 01 K −2.52957E+ −1.20217E+ K −6.69965E+−1.39708E− D2 0.00000E+ −7.11965E−03 D2 −1.50314E−03 1.50729E−03 00 0000 01 00 B4 3.61254E− 1.49085E− B4 −1.63400E− −2.24876E− D4 0.00000E+3.95789E−05 D4 3.61267E−06 −4.37989E−06 05 05 05 05 00 B6 −8.09230E−4.08194E− B6 1.64210E− 2.67132E− D6 0.00000E+ −7.31415E−08 D69.01459E−10 7.77917E−09 08 08 08 08 00 B8 0.00000E+ −1.20672E− B8−4.36204E− −2.94646E− D8 0.00000E+ −4.99893E−13 D8 −8.13695E−14−6.41723E−12 00 10 12 11 00 B10 0.00000E+ 0.00000E+ B10 −2.17220E−2.28464E− D10 0.00000E+ 0.00000E+ D10 −3.56630E−15 1.95495E−15 00 00 1514 00 B12 0.00000E+ 0.00000E+ B12 0.00000E+ −8.12057E− D12 0.00000E+0.00000E+00 D12 0.00000E+00 0.00000E+00 00 00 00 18 00

[0100] In the present embodiment the first fθ lens 6 aconsists of anegative meniscus lens with a concave surface opposed to the polygonmirror 5 in the sub-scanning section and the second fθ lens 6 b consistsof a positive meniscus lens with a concave surface opposed to thepolygon mirror 5 in the sub-scanning section. This structure permits thesub-scanning magnification to be decreased to a small value even in thesame positional layout.

[0101] In the present embodiment the sub-scanning magnification|β_(s)|=3.1.

[0102] In the incidence surface 6 ai of the first fθ lens 6 a, thesurface in the sub-scanning direction consists of a sagittal asymmetricchange surface in which the curvatures in the sagittal direction changeon an asymmetric basis in the main scanning direction with respect tothe optical axis.

[0103] Further, the magnitude relation among the curvatures in thesagittal direction is as follows.

[0104] curvatures on the light source side>curvature on the opticalaxis=curvatures on the anti-source side

[0105] Therefore, the surface is also a sagittal deformation surface inwhich the magnitude relation differs among the curvatures in thesagittal direction at the respective positions in the main scanningdirection with respect to the optical axis.

[0106] In the exit surface 6 ao of the first fθ lens 6 a, the surface inthe sub-scanning direction consists of a sagittal asymmetric changesurface in which the curvatures in the sagittal direction change on anasymmetric basis in the main scanning direction with respect to theoptical axis.

[0107] Further, the magnitude relation among the curvatures in thesagittal direction is as follows.

[0108] curvatures on the light source side>curvature on the opticalaxis>curvatures on the anti-source side

[0109] Thus, the surface is also a sagittal deformation surface in whichthe magnitude relation differs among the curvatures in the sagittaldirection at the respective positions in the main scanning directionwith respect to the optical axis.

[0110] In the incidence surface 6 bi of the second fθ lens 6 b, thesurface in the sub-scanning direction consists of a sagittal asymmetricchange surface in which the curvatures in the sagittal direction changeon an asymmetric basis in the main scanning direction with respect tothe optical axis and is also a sagittal deformation surface in which thecurvatures in the sagittal direction gradually increase on the side oflight source means 1 with respect to the optical axis but the curvaturesin the sagittal direction first decrease to an inflection point midwayand then gradually increase thereafter on the anti-source side.

[0111] In the exit surface 6 bo of the second fθ lens 6 b, the surfacein the sub-scanning direction consists of a surface in which thecurvatures in the sagittal direction increase on a symmetric basis inthe main scanning direction on either side of the optical axis.

[0112]FIG. 12 is an aberration diagram to show the curvature of field inthe sub-scanning direction and ratios of sub-scanning magnifications ofthe optical scanning apparatus in the present embodiment.

[0113] In the present embodiment, similarly as in above Embodiment 2, aplurality of surfaces are used to effect such bending as to make thechange in the curvatures in the sagittal direction inclined in the samedirection, whereby the asymmetry of sub-scanning magnifications and thecurvature of field in the sub-scanning direction can be corrected wellsimultaneously even in the case of the wide angles of view and the highsub-scanning magnifications.

[0114] It is needless to mention that the configurations in aboveEmbodiments 2, 3 can also be applied to the optical scanning apparatususing a single optical beam.

[0115]FIG. 14 is a cross-sectional view of the principal part along thesub-scanning direction to show an embodiment of the image-formingapparatus of the present invention. In FIG. 14, numeral 104 designatesthe image-forming apparatus. This image-forming apparatus 104 acceptsinput of code data Dc from an external device 117 such as a personalcomputer or the like. This code data Dc is converted into image data(dot data) Di by a printer controller 111 in the apparatus. This imagedata Di is supplied to an optical scanning unit 100 having the structureas described in either of Embodiments 1 to 3. This optical scanning unit100 outputs an optical beam 103 modulated according to the image data Diand this light beam 103 scans a photosensitive surface of photosensitivedrum 101 in the main scanning direction.

[0116] The photosensitive drum 101 as an electrostatic latent imagecarrier (photosensitive body) is rotated clockwise by a motor 115. Withthe rotation thereof, the photosensitive surface of the photosensitivedrum 101 moves in the sub-scanning direction perpendicular to the mainscanning direction, relative to the light beam 103. Above thephotosensitive drum 101, a charging roller 102 for uniformly chargingthe surface of the photosensitive drum 101 is disposed so as to contactthe surface. Then the surface of the photosensitive drum 101 charged bythe charging roller 102 is exposed to the light beam 103 under scanningby the optical scanning unit 100.

[0117] As described previously, the light beam 103 is modulated based onthe image data Di and an electrostatic latent image is formed on thesurface of the photosensitive drum 101 under irradiation with this lightbeam 103. This electrostatic latent image is developed into a tonerimage by a developing unit 107 disposed so as to contact thephotosensitive drum 101 downstream in the rotating direction of thephotosensitive drum 101 from the irradiation position of the light beam101.

[0118] The toner image developed by the developing unit 107 istransferred onto a sheet 112 being a transfer medium, by a transferroller 108 opposed to the photosensitive drum 101 below thephotosensitive drum 101. Sheets 112 are stored in a sheet cassette 109in front of (i.e., on the right side in FIG. 14) of the photosensitivedrum 101, but sheet feed can also be implemented by hand feeding. Asheet feed roller 110 is disposed at an end of the sheet cassette 109and feeds each sheet 112 in the sheet cassette 109 into the conveyancepath.

[0119] The sheet 112 onto which the toner image unfixed was transferredas described above, is further transferred to a fixing unit locatedbehind the photosensitive drum 101 (i.e., on the left side in FIG. 14).The fixing unit is composed of a fixing roller 113 having a fixingheater (not illustrated) inside and a pressing roller 114 disposed inpress contact with the fixing roller 113 and heats while pressing thesheet 112 thus conveyed from the transfer part, in the nip part betweenthe fixing roller 113 and the pressing roller 114 to fix the unfixedtoner image on the sheet 112. Sheet discharge rollers 116 are disposedfurther behind the fixing roller 113 to discharge the fixed sheet 112 tothe outside of the image-forming apparatus.

[0120] Although not illustrated in FIG. 14, the print controller 111also performs control of each section in the image-forming apparatus,including the motor 115, and control of the polygon motor etc. in theoptical scanning unit described above, in addition to the conversion ofdata described above.

[0121] Further, the present invention may also be applied toconfigurations in which sagittal asymmetric change surfaces are laid onfour or more surfaces of lenses constituting the fθ lenses.

[0122] In Embodiments 2, 3 the number of the light-emitting regions ofthe light source means was two, but the present invention can also beapplied to a plurality of light-emitting regions not less than three.

[0123] According to the present invention, the optical scanning means isconstructed of a plurality of sagittal asymmetric change surfaces andthe shape of each lens is properly set in the optical scanning apparatusin which light is incident at angles in the main scanning direction tothe deflecting means as described previously, whereby good correctioncan be made for the asymmetry of the sub-scanning magnifications and thecurvature of field in the sub-scanning direction occurring in the casewherein the deflecting means is the rotary polygon mirror. This canaccomplish the compact, high-definition, optical scanning apparatuscapable of keeping the spot size uniform in the sub-scanning directionthroughout the entire, effective scanning area on the surface to bescanned.

[0124] According to the present invention, the scanning optical means isconstructed of a plurality of sagittal asymmetric change surfaces andthe shape of each lens is properly set in the multi-beam opticalscanning apparatus as described above, whereby the invention canaccomplish the compact, high-definition, multi-beam optical scanningapparatus without pitch irregularity capable of keeping the line pitchintervals in the sub-scanning direction constant throughout the entire,effective scanning area.

What is claimed is:
 1. An optical scanning apparatus comprising entranceoptical means for guiding light emitted from light source means, todeflecting means, and scanning optical means for focusing the lightreflectively deflected by the deflecting means, on a surface to bescanned, wherein the scanning optical means comprises a plurality ofsagittal asymmetric change surfaces in which curvatures in the sagittaldirection change on an asymmetric basis in the meridional direction withrespect to the optical axis of the scanning optical means.
 2. Theoptical scanning apparatus according to claim 1, wherein said sagittalasymmetric change surfaces comprise two or more sagittal modificationsurfaces in which magnitude relation differs among curvatures in thesagittal direction at respective positions in the meridional directionwith respect to the optical axis.
 3. The optical scanning apparatusaccording to claim 2, wherein said sagittal deformation surfacescomprise two or more surfaces in which the curvatures in the sagittaldirection at the respective positions in the meridional direction withrespect to the optical axis become large or small on the same side. 4.The optical scanning apparatus according to claim 2, wherein in at leastone surface of said sagittal deformation surfaces the curvatures in thesagittal direction become large on the side of said light source meanswith respect to the optical axis.
 5. The optical scanning apparatusaccording to claim 1, wherein in at least one surface of said sagittalasymmetric change surfaces the curvatures in the sagittal direction havean inflection point only on one side in the meridional direction withrespect to the optical axis.
 6. The optical scanning apparatus accordingto claim 1, wherein said scanning optical means comprises a plurality offθ lenses, an fθ lens located closest to the deflecting means out ofsaid plurality of fθ lenses has a negative, refractive power in thesub-scanning direction, and an fθ lens located closest to the surface tobe scanned has a positive, refractive power in the sub-scanningdirection.
 7. The optical scanning apparatus according to claim 6,wherein all lens surfaces of said plurality of fθ lenses are formed in aconcave shape opposed to said deflecting means.
 8. The optical scanningapparatus according to claim 1, wherein the following condition issatisfied: k/W≦0.6 where k is an fθ coefficient of said scanning opticalmeans and W an effective scanning width on said surface to be scanned.9. The optical scanning apparatus according to claim 1, wherein thefollowing condition is satisfied: |β_(s)|≧2 where β_(s) is a lateralmagnification in the sub-scanning direction of said scanning opticalmeans.
 10. A multi-beam optical scanning apparatus comprising lightsource means having a plurality of light-emitting regions, entranceoptical means for guiding a plurality of beams emitted from the lightsource means, to deflecting means, and scanning optical means forfocusing the plurality of beams reflectively deflected by the deflectingmeans, on a surface to be scanned, wherein said scanning optical meanscomprises a plurality of sagittal asymmetric change surfaces in whichcurvatures in the sagittal direction change on an asymmetric basis inthe meridional direction with respect to the optical axis of thescanning optical means.
 11. The multi-beam optical scanning apparatusaccording to claim 10, wherein said sagittal asymmetric change surfacescomprise two or more sagittal modification surfaces in which magnituderelation differs among curvatures in the sagittal direction atrespective positions in the meridional direction with respect to theoptical axis.
 12. The multi-beam optical scanning apparatus according toclaim 11, wherein said sagittal deformation surfaces comprise two ormore surfaces in which the curvatures in the sagittal direction at therespective positions in the meridional direction with respect to theoptical axis become large or small on the same side.
 13. The multi-beamoptical scanning apparatus according to claim 11, wherein in at leastone surface of said sagittal deformation surfaces the curvatures in thesagittal direction become large on the side of said light source meanswith respect to the optical axis.
 14. The multi-beam optical scanningapparatus according to claim 10, wherein in at least one surface of saidsagittal asymmetric change surfaces the curvatures in the sagittaldirection have an inflection point only on one side in the meridionaldirection with respect to the optical axis.
 15. The multi-beam opticalscanning apparatus according to claim 10, wherein said scanning opticalmeans comprises a plurality of fθ lenses, an fθ lens located closest tothe deflecting means out of said plurality of fθ lenses has a negative,refractive power in the sub-scanning direction, and an fθ lens locatedclosest to the surface to be scanned has a positive, refractive power inthe sub-scanning direction.
 16. The multi-beam optical scanningapparatus according to claim 15, wherein all lens surfaces of saidplurality of fθ lenses are formed in a concave shape opposed to saiddeflecting means.
 17. The multi-beam optical scanning apparatusaccording to claim 10, wherein the following condition is satisfied:k/W≦0.6 where k is an fθ coefficient of said scanning optical means andW an effective scanning width on said surface to be scanned.
 18. Themulti-beam optical scanning apparatus according to claim 10, wherein thefollowing condition is satisfied: |β_(s)|≧2 where β_(s) is a lateralmagnification in the sub-scanning direction of said scanning opticalmeans.
 19. An image-forming apparatus comprising the scanning opticalapparatus as set forth in either one of claims 1 to 18, a photosensitivebody located at said surface to be scanned, a developing unit fordeveloping an electrostatic, latent image formed on said photosensitivebody with the light under scan by said scanning optical apparatus, intoa toner image, a transfer unit for transferring said developed tonerimage onto a transfer medium, and a fixing unit for fixing thetransferred toner image on the transfer medium.
 20. An image-formingapparatus comprising the scanning optical apparatus as set forth ineither one of claims 1 to 18, and a printer controller for convertingcode data supplied from an external device, into an image signal andsupplying the image signal to said scanning optical apparatus.